=========================
Dry stable boundary layer
=========================

Background
------------------

This is the stable boundary layer scenario described by Sauer and Munoz-Esparza (2020). This the stable boundary layer scenario outlined in Kosovic and Curry (2000).

Input parameters
----------------

* Number of grid points: :math:`[N_x,N_y,N_z]=[128,126,122]`
* Isotropic grid spacings: :math:`[dx,dy,dz]=[3.125,3.125,3.125]` m
* Domain size: :math:`[0.40 \times 0.39 \times 0.38]` km
* Model time step: :math:`0.005` s
* Geostrophic wind: :math:`[U_g,V_g]=[8,0]` m/s
* Advection scheme: 5th-order upwind
* Time scheme: 3rd-order Runge Kutta
* Latitude: :math:`73^{\circ}` N
* Surface potential temperature: :math:`265` K
* Potential temperature profile:

.. math::
  \partial{\theta}/\partial z =
    \begin{cases}
      0 & \text{if $z$ $\le$ 100 m}\\
      0.01 & \text{if $z$ > 100 m}
    \end{cases}   

* Surface heat flux:  :math:`-0.25` K/h
* Surface roughness length: :math:`z_0=0.1` m
* Rayleigh damping layer: uppermost :math:`75` m of the domain
* Initial perturbations: :math:`\pm 0.25` K 
* Top boundary condition: free slip
* Lateral boundary conditions: periodic
* Time period: :math:`12` h

Execute FastEddy
----------------

1. Create a working directory to run the FastEddy tutorials and change to that directory.
2. Create a **Example03_SBL** subdirectory and change to that directory.
3. The FastEddy code will write its output to an **output** subdirectory. Create an **output** directory, if one does not already exist.   
4. Run FastEddy using the input parameters file *Example03_SBL.in* located in the **tutorials/examples/** subdirectory of the FastEddy repository. 

See :ref:`run_fasteddy` for instructions on how to build and run FastEddy on NSF NCAR's High Performance Computing machines.

Visualize the output
--------------------

1. Open the Jupyter notebook entitled *MAKE_FE_TUTORIAL_PLOTS.ipynb*.
2. Under the "Define parameters" section, modify :code:`path_base`, specifying the full path to the **Example03_CBL** subdirectory, but don't include the **Example03_CBL** subdirectory. Be sure to include a trailing slash :code:`/`).
3. Under the "Define parameters" section, modify :code:`case` to set its value to :code:`stable`.
4. Run the Jupyter notebook.
5. The resulting XY cross section png plots will be placed in a **FIGS** subdirectory of the **Example03_CBL** directory.

XY-plane views of instantaneous velocity components at :math:`t=12` h (FE_SBL.8640000):

.. image:: ../images/UVWTHETA-XY-stable.png
  :width: 1200
  :alt: Alternative text
  
XZ-plane views of instantaneous velocity components at :math:`t=12` h (FE_SBL.8640000):

.. image:: ../images/UVWTHETA-XZ-stable.png
  :width: 600
  :alt: Alternative text
  
Mean (domain horizontal average) vertical profiles of state variables at :math:`t=12` h (FE_SBL.8640000):

.. image:: ../images/MEAN-PROF-stable.png
  :width: 750
  :alt: Alternative text
  
Horizontally-averaged vertical profiles of turbulence quantities at :math:`t=11-12` h (FE_TEST.8640000) [perturbations are computed at each point relative to the previous 1-hour mean, and then horizontally averaged]:

.. image:: ../images/TURB-PROF-stable.png
  :width: 1200
  :alt: Alternative text

Analyze the output
------------------

* Using the XY and XZ cross sections, discuss the characteristics (scale and magnitude) of the resolved turbulence.
* What is the boundary layer height in the stable case?
* Using the vertical profile plots, explain why the boundary layer is stable.